Method of operating a network using differentiated pricing and a network configured to operate using differentiated pricing

ABSTRACT

The method of operating a network includes receiving a measurement of total traffic intensity, receiving an expected quality of service associated with a packet, and assigning the packet to one of two or more priority queues based on the measurement of total traffic intensity and the expected quality of service, the two or more priority queues having different delay metrics.

BACKGROUND

The amount of data traffic generated by mobile terminals connected towireless networks continues to increase as technology progresses.However, the revenue generated from the mobile terminals has notincreased at the same pace as costs of serving the mobile terminals.Previous data plans offered unlimited data traffic for a flat rate,while current data plans offer tiers of data usage at varying pricesthat allow a fixed amount of data per month. Despite this change, theprice that users of the mobile terminals are willing to pay per Megabyteof data traffic is decreasing and the revenue generated from the currentfixed data plans may not offset the costs of growing and serving thewireless networks. More efficient methods of operating the wirelessnetworks in order to increase revenue and/or decrease the cost ofserving the mobile terminals are desired.

SUMMARY

At least one example embodiment is directed to a method of operating anetwork using differentiated pricing and/or a network configured tooperate using differentiated pricing.

According to at least one example embodiment, a method of operating anetwork includes receiving a measurement of total traffic intensity;receiving an expected quality of service associated with a packet; andassigning the packet to one of two or more priority queues based on themeasurement of total traffic intensity and the expected quality ofservice, the two or more priority queues having different delay metrics.

The method may include servicing the packet from the one of the two ormore priority queues.

The method may include measuring the total traffic intensity, and thereceiving receives the measured total traffic intensity.

The method may include determining a traffic intensity associated witheach of the two or more priority queues and the delay metric associatedwith each of the two or more priority queues based on the measurement oftotal traffic intensity, and the assigning assigns the packet to the oneof two or more priority queues based on the expected quality of serviceand the determined traffic intensity associated with each of the two ormore priority queues.

The expected quality of service may include a requested priority from auser, the requested priority being two or more priority levels that theuser selects.

The receiving the expected quality of service associated with the packetmay include receiving an expected quality of service associated with amobile terminal; receiving the packet from the mobile terminal; andassociating the packet with the expected quality of service associatedwith the mobile terminal.

The method may include determining a price of service for the packetbased on the determined the delay metric associated with the one of twoor more priority queues.

The delay metric may be an average delay and the determining determinesthe average delay based on an average service time and an averagewaiting time.

The delay metric may be a P-th percentile delay and the determiningdetermines the P-th percentile delay based on a probabilityapproximation including a waiting time for the one of two or morepriority queues, a number of components of a probability mass function(PMF) associated with a service time, and a resolution of the PMFassociated with the service time.

The delay metric may be a truncated average delay approximation and thedetermining determines the truncated average delay approximation basedon a waiting time for the one of two or more priority queues and a delayfor the non-prioritized system.

According to at least one example embodiment, a network includes a queuecontroller configured to receive a measurement of total trafficintensity, to receive an expected quality of service associated with apacket, and to assign the packet to one of two or more priority queuesbased on the measurement of total traffic intensity and the expectedquality of service, the two or more priority queues having differentdelay metrics.

The network may also include a buffer configured to service the packetfrom the one of two or more priority queues.

The network may also include a traffic intensity measurement deviceconfigured to measure the total traffic intensity and to transmit thetotal traffic intensity to the queue controller.

The queue controller may be further configured to determine a trafficintensity associated with each of the two or more priority queue and thedelay metric associated with each of the two or more priority queuesbased on the measurement of total traffic intensity, and the queuecontroller is configured to assign the packet to the one of two or morepriority queues based on the expected quality of service and thedetermined traffic intensity associated with each of the two or morepriority queues.

The expected quality of service may include a requested priority from auser, the requested priority being two or more priority levels that theuser selects.

The queue controller may be further configured to receive an expectedquality of service associated with a mobile terminal, to receive thepacket from the mobile terminal and to associate the packet with theexpected quality of service associated with the mobile terminal.

The queue controller may be configured to determine a price of servicefor the packet based on the determined delay metric associated with theone of two or more priority queues.

The delay metric may be an average delay and the queue controller isconfigured to determine the average delay based on an average servicetime and an average waiting time.

The delay metric may be a P-th percentile delay and the queue controlleris configured to determine the P-th percentile delay based on aprobability approximation including a waiting time for the one of two ormore priority queues, a number of components of a probability massfunction (PMF) associated with a service time, and a resolution of thePMF associated with the service time.

The delay metric may be a truncated average delay approximation and thequeue controller is configured to determine the truncated average delayapproximation based on a waiting time for the one of two or morepriority queues and a delay for the non-prioritized system.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments will become more fully understood from the detaileddescription given herein below and the accompanying drawings, whereinlike elements are represented by like reference numerals, which aregiven by way of illustration only and thus are not limiting of thepresent invention, and wherein:

FIG. 1 illustrates a base station that includes a computer system, thebase station connecting mobile terminals in a coverage area of the basestation to a wireless network, according to some example embodiments;

FIG. 2 illustrates an example structure of the computer system,according to some example embodiments;

FIG. 3 is a flowchart illustrating a method of determining the trafficintensity associated with each priority queue and a delay metricassociated with each priority queue, according to some exampleembodiments;

FIG. 4 is a flowchart illustrating a method of assigning each mobileterminal to a priority queue, according to some example embodiments; and

FIG. 5 is a flowchart illustrating a method of placing a data requestfrom a mobile terminal in the assigned priority queue associated withthe mobile terminal, according to some example embodiments.

It should be noted that these figures are intended to illustrate thegeneral characteristics of methods, structure and/or materials utilizedin certain example embodiments and to supplement the written descriptionprovided below. These drawings are not, however, to scale and may notprecisely reflect the precise structural or performance characteristicsof any given example embodiment, and should not be interpreted asdefining or limiting the range of values or properties encompassed byexample embodiments. For example, the relative thicknesses andpositioning of molecules, layers, regions and/or structural elements maybe reduced or exaggerated for clarity. The use of similar or identicalreference numbers in the various drawings is intended to indicate thepresence of a similar or identical element or feature.

DETAILED DESCRIPTION

Example embodiments will now be described more fully with reference tothe accompanying drawings, in which some example embodiments are shown.Example embodiments may, however, be embodied in many different formsand should not be construed as being limited to the example embodimentsset forth herein; rather, these example embodiments are provided so thatthis disclosure will be thorough and complete, and will fully convey theconcept of example embodiments to those of ordinary skill in the art. Inthe drawings, the thicknesses of layers and regions are exaggerated forclarity. Like reference numerals in the drawings denote like elements,and thus their description will be omitted.

It will be understood that, although the terms “first”, “second”, etc.may be used herein to describe various elements, components, and/orsections, these elements, components, and/or sections should not belimited by these terms. These terms are only used to distinguish oneelement, component or section from another element, component, orsection. Thus, a first element, component, or section discussed belowcould be termed a second element, component, or section withoutdeparting from the teachings of example embodiments.

The terminology used herein is for the purpose of describing particularexample embodiments only and is not intended to be limiting of exampleembodiments. As used herein, the singular forms “a,” “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. It will be further understood that the terms“comprises”, “comprising”, “includes” and/or “including,” if usedherein, specify the presence of stated features, integers, steps,operations, elements and/or components, but do not preclude the presenceor addition of one or more other features, integers, steps, operations,elements, components and/or groups thereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Portions of the present invention and corresponding detailed descriptionare presented in terms of software, or algorithms and symbolicrepresentations of operations on data bits within a computer memory.These descriptions and representations are the ones by which those ofordinary skill in the art effectively convey the substance of their workto others of ordinary skill in the art. An algorithm, as the term isused here, and as it is used generally, is conceived to be aself-consistent sequence of steps leading to a desired result. The stepsare those requiring physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofoptical, electrical, or magnetic signals capable of being stored,transferred, combined, compared, and otherwise manipulated. It hasproven convenient at times, principally for reasons of common usage, torefer to these signals as bits, values, elements, symbols, characters,terms, numbers, or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise, or as is apparent from the discussion,terms such as “processing” or “computing” or “calculating” or“determining” or “displaying” or the like, refer to the action andprocesses of a computer system, or similar electronic computing device,that manipulates and transforms data represented as physical, electronicquantities within the computer system's registers and memories intoother data similarly represented as physical quantities within thecomputer system memories or registers or other such information storage,transmission or display devices.

Some example embodiments will now be described with reference to theattached figures. Various structures, systems and devices areschematically depicted in the drawings for purposes of explanation onlyand so as to not obscure the present invention with details that arewell known to those skilled in the art. Nevertheless, the attacheddrawings are included to describe and explain some illustrative exampleembodiments. The words and phrases used herein should be understood andinterpreted to have a meaning consistent with the understanding of thosewords and phrases by those skilled in the relevant art. No specialdefinition of a term or phrase, i.e., a definition that is differentfrom the ordinary and customary meaning as understood by those skilledin the art, is intended to be implied by consistent usage of the term orphrase herein. To the extent that a term or phrase is intended to have aspecial meaning, i.e., a meaning other than that understood by skilledartisans, such a special definition will be expressly set forth in thespecification in a definitional manner that directly and unequivocallyprovides the special definition for the term or phrase.

As used herein, the term “mobile terminal” may be considered synonymousto, and may hereafter be occasionally referred to, as a phone,wirelessly equipped laptop, a mobile, mobile unit, mobile user,subscriber, user, remote station, access terminal, receiver, etc., andmay describe a remote user of wireless resources in a wireless network.The term “base station” (BS) may be considered synonymous to and/orreferred to as a base transceiver station (BTS), Node B, etc. and maydescribe equipment that provides data and/or voice connectivity betweena wireless network and one or more users.

FIG. 1 illustrates a base station 110 that includes a computer system120, the base station 110 connecting mobile terminals 130 in a coveragearea of the base station 110 to a wireless network 100, according tosome example embodiments.

When a mobile terminal 130 is connected to the base station 110, themobile terminal 130 may send a data request to wirelessly exchangepackets of data with the base station 110. For example, the mobileterminal 130 may send a data request to wirelessly send packets of datato the base station 110 to upload data or send a data request towirelessly receive packets of data from the base station 110 to downloaddata. The base station 110 may relay the packets of data to the wirelessnetwork 100 or a larger network, such as the internet. The base station110 may receive packets of data from the wireless network 100 or thelarger network and relay the received packets of data to the mobileterminal 130. The computer system 120 may control the relay of datapackets, as discussed below with regard to FIGS. 2-3.

The example embodiments illustrated in FIG. 1 show a single base station110 that includes a computer system 120. However, example embodimentsare not limited thereto, and a base station 110 may be collocated withan external computer system 120 or multiple base stations 110 may be incommunication with a single computer system 120.

FIG. 2 illustrates an example structure of the computer system 120,according to some example embodiments. The computer system 120 mayinclude a traffic intensity measurement device 205, a queue controller210 and a buffer 220. The queue controller 210 may include a switch 212and a controller 214.

The total traffic requested by mobile terminals 130 is input to thecomputer system 120. The total traffic requested by mobile terminals 130may include all data requests by mobile terminals 130 within a coveragearea of the base station 110 to upload or download packets of data. Thetraffic intensity measurement device 205 may measure the total trafficrequested by mobile terminals 130 and provide the controller 214 with ameasurement of the total traffic intensity (λ_(b)). The measurement oftotal traffic intensity (λ_(b)) may be in packets/second,Megabytes/second or other measurements for a rate of data.

The controller 214 may receive an expected quality of service for allmobile terminals 130 active in the coverage area of the base station110. A mobile terminal 130 is considered active if the mobile terminal130 is connected to the base station 110.

Based on the expected quality of service for a mobile terminal 130, thecontroller 214 may associate one of several priority queues with themobile terminal 130. The switch 212 may assign data requests from themobile terminal 130 to the priority queue associated with the mobileterminal 130.

The buffer 220 may buffer the assigned data requests until the assigneddata requests are serviced and the data requests or packets may beserviced based on the priority queue. For example, the buffer 220 mayservice all of the data requests or packets in the first priority queuebefore servicing any of the data requests or packets in the secondpriority queue.

The computer system 120 may output prioritized traffic, which indicatesthe order in which each data request from the mobile terminals 130 willbe serviced or processed by the base station 110.

FIG. 3 is a flowchart illustrating a method of determining the trafficintensity associated with each priority queue and a delay metricassociated with each priority queue, according to some exampleembodiments.

In S310, the queue controller 210 may receive a measurement of the totaltraffic intensity (λ_(b)). For example, the queue controller 210 mayreceive a measurement of the total traffic intensity (λ_(b)) from thetraffic intensity measurement device 205. Alternatively, the queuecontroller 210 may receive a measurement of the total traffic intensity(λ_(b)) from a source external to the computer system 120, such as fromthe base station 110 or from another device in the wireless network 100.As discussed above, the total traffic intensity (λ_(b)) may be ameasurement [for example, packets/second] of the total traffic requestedby mobile terminals 130 including all data download requests or dataupload requests.

In S320, the queue controller 210 may determine the traffic intensityassociated with each priority queue (λ₁, λ₂ . . . , λ_(N)) and a delaymetric associated with each priority queue. The delay metric associatedwith each priority queue may be based on the traffic intensitiesassociated with each priority queue (λ₁, λ₂ . . . , λ_(N)) and mayindicate a delay time for an individual data request to be serviced. Forexample, the total traffic intensity (λ_(b)) may be fragmented and itsfractions may be assigned to four different priority queues (λ₁, λ₂, λ₃,λ₄). The sum of traffic intensities associated with each priority queue(λ₁, λ₂, λ₃, λ₄) is equal to the total traffic intensity (λ_(b)). Basedon the traffic intensity associated with each priority queue (λ₁, λ₂,λ₃, λ₄), each priority queue may have a different delay metric.

The queue controller 210 may determine the traffic intensity associatedwith each priority queue (λ₁, λ₂ . . . , λ_(N)) using the equationsdiscussed below with reference to Pricing Policies 1-3. Pricing Policies1-3 may relate a delay metric associated with each priority queue with aprice of service, as will be discussed in greater detail below. Thetraffic intensity associated with each priority queue (λ₁, λ₂ . . . ,λ_(N)) may be used as the optimal distribution of mobile terminals 130amongst the priority queues. For example, the queue controller 210 maydetermine that the optimal distribution of mobile terminals 130 amongthe priority queues is 40% in a first priority queue, 27% in a secondpriority queue, 19% in a third priority queue and 14% in a fourthpriority queue based on the traffic intensity associated with eachpriority queue (λ₁, λ₂ . . . , λ_(N)) calculated using Pricing Policy 2.Use of the determined optimized distribution will be discussed ingreater detail below with reference to S420 of FIG. 4.

The queue controller 210 may determine the delay metric associated witheach priority queue using the equations discussed below with referenceto Pricing Policies 1-3. The delay metric may depend on which PricingPolicy is chosen. For example, the delay metric may depend on a waitingtime and a service time. The waiting time is the time spent by a datarequest in the buffer 220 prior to being serviced, while the servicetime is the time required for servicing the data request. The waitingtime may depend on a quantity of data requests already in the priorityqueue and a quantity of data requests in any priority queue with ahigher priority.

The queue controller 210 may determine the traffic intensity associatedwith each priority queue (λ₁, λ₂ . . . , λ_(N)) and the delay metricassociated with each priority queue periodically. For example, the queuecontroller 210 may determine these values every 10 milliseconds, or thequeue controller 210 may determine these values every 10 minutes.However, example embodiments are not limited thereto, and the queuecontroller 210 may use any desired period of time. Alternatively, thequeue controller 210 may determine these values dynamically. However,determining the values dynamically may consume more resources.

As an alternative to using the equations of Pricing Policies 1-3, thequeue controller 210 may determine the traffic intensity associated witheach priority queue (λ₁, λ₂ . . . , λ_(N)) and the delay metricassociated with each priority queue based on a lookup table. Forexample, the equations discussed below with reference to PricingPolicies 1-3 may be solved and quantized in the lookup table, and thequeue controller 210 may find the traffic intensity associated with eachpriority queue (λ₁, λ₂ . . . , λ_(N)) in the lookup table based on thetotal traffic intensity (λ_(b)). As an example, the lookup table mayhave a range of traffic intensities (λ_(b)) from 1 MB/s to 100 MB/s,with a quantization of 1 MB/s. Thus, if the total traffic intensity(λ_(b)) is between 1-2 MB/s, the lookup table may provide a firsttraffic intensity associated with each priority queue (λ₁, λ₂ . . . ,λ_(N)), whereas if the total traffic intensity (λ_(b)) is between 2-3MB/s, the lookup table may provide a second traffic intensity associatedwith each priority queue (λ₁, λ₂ . . . , λ_(N)).

FIG. 4 is a flowchart illustrating a method of assigning each mobileterminal to a priority queue, according to some example embodiments.

The queue controller 210 may receive an expected quality of service inS410. For example, the queue controller 210 may receive an expectedquality of service from any active mobile terminals 130 connected to thebase station 110. A list of all active mobile terminals 130 connected tothe base station 110 may be included in a table stored in the basestation 110. Alternatively, the list of all active mobile terminals maybe included in a table stored elsewhere in the wireless network 100.

The expected quality of service may be included with a data request ordata packet from the mobile terminal 130 or the expected quality ofservice may be received separately and associated with the mobileterminal 130. The expected quality of service may be based on the dataplan associated with the mobile terminal 130 or, alternatively, theexpected quality of service may be based on a requested priority from auser of the mobile terminal 130, the requested priority being two ormore priority levels that the user selects.

The expected quality of service may be, for example, a unitless valuethat the mobile terminal 130 requests indicating a level of importanceof shorter delays or lower prices. For example, the expected quality ofservice associated with the mobile terminal 130 may be a priority levelfrom 1-100 based on the price a user of the mobile terminal 130 wants topay or the delay the user wants to experience, with 1 indicating themobile terminal 130 is requesting the longest delay (and thereforelowest price) and 100 indicating the mobile terminal 130 is requestingthe shortest delay (and therefore highest price). Example embodimentsare not limited thereto, and the expected quality of service may bebased on other methods. The process of setting prices for service isdiscussed in greater detail below with regard to Pricing Policies 1-3.

If the expected quality of service is based on the data plan associatedwith the mobile terminal 130, all data packets or data requests from themobile terminal 130 may have the same expected quality of service.Therefore, the queue controller 210 may associate this expected qualityof service with every data request from the mobile terminal 130.

Alternatively, if the expected quality of service is based on arequested priority from a user of the mobile terminal 130, the user maydynamically change the expected quality of service based on a desiredspeed or importance. For example, the user may request a higher prioritywhile performing work-related functions and request a lower prioritywhile performing non-work-related functions. The higher priority willoffer faster service, but the price of service will increaseaccordingly, as discussed below with regard to Pricing Policies 1-3.

The queue controller 210 may store the expected quality of serviceassociated with the mobile terminal 130 or communicate with the basestation 110 or another device to determine the expected quality ofservice associated with the mobile terminal 130.

In S420, the queue controller 210 may assign a first mobile terminal 130to a priority queue based on the measurement of total traffic intensity(λ_(b)) and the expected quality of service for the first mobileterminal 130. For example, the queue controller 210 may use the trafficintensity associated with each priority queue (λ₁, λ₂ . . . , λ_(N))determined in S320 as the optimal distribution of mobile terminals 130amongst the priority queues. Based on the optimal distribution of mobileterminals 130 amongst the priority queues, the queue controller 210 maycompare the expected quality of service for the first mobile terminal130 with the expected quality of service of all other mobile terminals130 to assign the first mobile tenninal 130 to a particular priorityqueue.

As an example, the queue controller may determine that the optimaldistribution of mobile terminals 130 has 40% of the mobile terminals 130assigned to a first priority queue. If the expected quality of servicefor the first mobile terminal 130 is in the top 30% of expected qualityof services for all active mobile terminals 130, the queue controller210 may assign the first mobile terminal 130 to the first priorityqueue. However, if the expected quality of service for the first mobileterminal 130 is between 50% and 60% of expected quality of services forall active mobile terminals 130, the queue controller 210 may assign thefirst mobile terminal 130 to the second priority queue.

As discussed above with reference to S320 and below with reference toPricing Policies 1-3, the optimal distribution of mobile terminals 130may vary depending on the Pricing Policy or delay metric used. Moreover,the queue controller 210 may rely on a lookup table or may calculate thetraffic intensity associated with each priority queue (λ₁, λ₂ . . . ,λ_(N)) as necessary. If using the lookup table, the queue controller 210may use the measured total traffic intensity (λ_(b)) to determine theoptimal distribution and/or an estimated delay metric associated witheach priority queue.

FIG. 5 is a flowchart illustrating a method of placing a data requestfrom a mobile terminal 130 in the assigned priority queue associatedwith the mobile terminal 130, according to some example embodiments.

In S510, the queue controller 210 may receive a data request from amobile terminal 130, such as a data request to upload or downloadpackets of data. In S520, the queue controller may place the datarequest in the priority queue associated with the mobile terminal 130that was assigned in S420. In S530, the buffer 220 may service the datarequest based on the assigned priority queue.

As an example, the queue controller 210 may receive a first data requestfrom a first mobile terminal 130. Previously, the first mobile terminal130 was assigned to the first priority queue. Therefore, the queuecontroller 210 may place the first data request from a first mobileterminal 130 in a first priority queue in the buffer 220. As the firstdata request is in the first priority queue, as soon as all data requestalready in the first priority queue are serviced, the buffer 220 mayservice the first data request.

As discussed above referring to S410, a user of the mobile terminal 130may dynamically change the expected quality of service based on adesired speed or importance. Therefore, the queue controller 210 mayreceive a second expected quality of service from the mobile terminal130 and assign the mobile terminal 130 to a second priority queuesimultaneously to performing steps S510-S530. Thus, a second datarequest from the first mobile terminal 130 may be placed in a differentpriority queue from the first data request from the first mobileterminal 130. Example embodiments are not limited thereto, and the queuecontroller 210 may move the first data request to a different priorityqueue if the mobile terminal 130 is assigned to a different priorityqueue prior to the first request being serviced by the buffer 220.

The buffer 220 may service the data requests or packets based on thepriority queue. For example, the buffer 220 may service all of the datarequests or packets in the first priority queue before servicing any ofthe data requests or packets in the second priority queue. Similarly,the buffer 220 may service all of the data requests or packets in thesecond priority queue before servicing any of the data requests orpackets in the third priority queue. In this way, the higher thepriority queue, the faster the buffer 220 services the data requests orpackets. This is an example of a delay system.

Due to the delay system, a delay metric associated with each priorityqueue may depend on the total traffic intensity (λ_(b)) and may indicatea delay time for an individual data request to be serviced. For example,because the buffer 220 may service all of the data requests or packetsin the first priority queue before servicing any of the data requests orpackets in the second priority queue, the second priority queue has adelay due to the number of data requests or packets currently in thefirst priority queue and any additional data requests or packetsreceived by the first priority queue. If the total traffic intensity(λ_(b)) is low, which may reflect a low load on the base station 110,the last priority queue may have a delay metric similar to a delaymetric for the first priority queue. However, if the total trafficintensity (λ_(b)) is high, which may reflect a high load on the basestation 110, the last priority queue may have a delay metric far longerthan a delay metric for the first priority queue.

Non-preemptive priority queues or preemptive priority queues may beused. In a priority queue, a data request with a lower priority is onlyserviced when there are no data requests with higher priority levels inthe system. In a non-preemptive system, once the processing of a datarequest or packet has started, it is allowed to carry on to completioneven if data requests or packets of higher priority levels arrive at thesystem in the intervening time. In contrast, a preemptive systemimmediately suspends the processing of a lower-priority data request orpacket when a high-priority data request or packet arrives.

As discussed above, a delay metric associated with each priority queuemay be used to calculate a price of service for each data request, aswill be discussed in greater detail below with reference to PricingPolicies 1-3.

Price of Service

The computer system 120 may translate typical network quantities, suchas delay in seconds, into monetary quantities, such as $/packet or$/Byte. To calculate the price of service, the computer system 120 mayconsider revenue to be proportional to a total traffic intensity (λ_(b))over the delay metric, the total traffic intensity (λ_(b)) being therate at which data requests arrive at the computer system 120.

$\begin{matrix}{{Revenue} \propto \frac{{Total}\mspace{14mu} {Traffic}\mspace{14mu} {{Intensity}\left( \lambda_{b} \right)}}{{Delay}\mspace{14mu} {Metric}}} & (1)\end{matrix}$

Similarly, the queue controller 210 may determine a price of service ofa single data request based on the delay metric of the assigned priorityqueue for the data request. For example, the computer system 120 may usean inverse pricing function, such as P_(n)=c/T_(n), where P_(n) is theprice for a packet [$/packet], T_(n) is the delay [seconds] and c is ascalar constant for the network [$·seconds/packet].

Below, three examples of potential pricing policies used to define thedelay metric and corresponding price of service for each data requestare discussed. Based on the pricing policy, the distribution of themobile terminals 130 in each priority queue may be optimized to increaserevenue or reduce future network expansion costs by reducing bandwidthfrom the baseline system. For example, the traffic intensity associatedwith each priority queue (λ₁, λ₂ . . . , λ_(N)) calculated using PricingPolicies 1-3 may be used as the optimal distribution of mobile terminals130 amongst the priority queues. The optimized distributions aredetermined in S320 and used in S420, discussed in greater detail above.

Pricing Policy 1—Average Delay:

For example, the average delays T_(n) for the priority queues n=1, 2, .. . , N may be used as the delay metrics. As is discussed in greaterdetail below with reference to equations (2)-(8), the queue controller210 may determine the average delay based on an average service time andan average waiting time.

Pricing Policy 2—P-th percentile Delay:

For example, the P-th percentile delays T_(n) ^(P) for the priorityqueues n=1, 2, . . . , N may be used as the delay metrics. As isdiscussed in greater detail below with reference to equations (10)-(14),the queue controller 210 may determine the P-th percentile delay basedon a probability approximation, which may include a waiting time for thepriority queues, a number of components of a probability mass function(PMF) associated with a service time, and a resolution of the PMFassociated with the service time.

Pricing Policy 3—Percentile Truncated Average Delay:

For example, the truncated average delays T _(n) ^(P) for the priorityqueues n=1, 2, . . . , N up to the P-th percentile delay of the baselinenon-prioritized system may be used as the delay metrics. As is discussedin greater detail below with reference to equations (15)-(21), the queuecontroller 210 may determine the percentile truncated average delayapproximation based on a waiting time for the priority queues and adelay for the non-prioritized system.

Pricing Policy 1: Average Delay

From a network operator perspective, the variables that can becontrolled to achieve the desired results with respect to revenues arethe fractional traffic intensities (λ₁, λ₂ . . . , λ_(N)) impinging onthe distinct priority queues. Therefore, Policy 1 uses the averagedelays T₁, T₂, . . . , T_(N) as variables of the utility function:

$\begin{matrix}{{{maximize}\mspace{14mu} {U\left( {\lambda_{1},\ldots \mspace{14mu},\lambda_{N},T_{1},\ldots \mspace{14mu},T_{N}} \right)}\overset{\overset{Revenue}{}}{c{\sum\limits_{i = 1}^{N}\frac{\lambda_{i}}{T_{i}}}}}{over}} & (2) \\{{{\lambda_{n} \in {\mathbb{R}}^{+}},{n = 1},\ldots \mspace{14mu},N}{{subject}\mspace{14mu} {to}\text{:}}} & (3) \\{{\sum\limits_{i = 1}^{N}\lambda_{i}} = \lambda_{b}} & (4) \\{{B = {\alpha \cdot B_{b}}},{0 < \alpha \leq 1}} & (5) \\{{T_{n} = {\underset{\underset{{Average}\mspace{14mu} {Service}\mspace{14mu} {Time}}{}}{\overset{\_}{X_{n}}} + \underset{\underset{{Average}\mspace{14mu} {Waiting}\mspace{14mu} {Time}}{}}{\frac{\sum\limits_{i = 1}^{N}\left( {\lambda_{i} \cdot \overset{\_}{X_{i}^{2}}} \right)}{2 \cdot \left\lbrack {1 - {\sum\limits_{i = 1}^{n - 1}\left( {\lambda_{i} \cdot \overset{\_}{X_{i}}} \right)}} \right\rbrack \cdot \left\lbrack {1 - {\sum\limits_{i = 1}^{n}\left( {\lambda_{i} \cdot \overset{\_}{X_{i}}} \right)}} \right\rbrack}}}},{n = 1},\ldots \mspace{14mu},N,} & (6) \\{{\overset{\_}{X_{n}} = {{\left\{ \frac{F}{B \cdot S} \right\}} = {{\frac{F}{B} \cdot }\left\{ \frac{1}{S} \right\}}}},{n = 1},\ldots \mspace{14mu},N} & (7) \\{{\overset{\_}{X_{n}^{2}} = {{\left\{ \left( \frac{F}{B \cdot S} \right)^{2} \right\}} = {{\frac{F^{2}}{B^{2}} \cdot }\left\{ \left( \frac{1}{S} \right)^{2} \right\}}}},{n = 1},\ldots \mspace{14mu},{N.}} & (8)\end{matrix}$

In the policy above,

+ indicates all positive real numbers, E indicates the Expectationvalue, λ_(b) is the total traffic intensity in the non-prioritizedbaseline system in packets per second, B_(b) is the bandwidth of thenon-prioritized baseline system, α is a bandwidth scaling parameter thatconnects the bandwidth of the prioritized system B to the bandwidth ofnon-prioritized baseline system B_(b), c is a constant that turns theproportionality relation in (1) to an equality and is connected to thenetwork costs, F=320 KB is the size of the file being downloaded (whichmay be considered constant) and S is a random variable representing thespectral efficiency of the wireless network which may be determined bysimulation. For example, simulating a two-ring, tree-sectored wirelessnetwork with wraparound, path-loss and shadow fading, uniform mobileterminal 130 distribution, and full-power transmission at each sector,we obtain:

$\begin{matrix}{{\left\{ \frac{1}{S} \right\}} \approx {0.81\mspace{14mu} {and}\mspace{14mu} \left\{ \left( \frac{1}{S} \right)^{2} \right\}} \approx {1.04.}} & (9)\end{matrix}$

However, these equations are provided to illustrate a particular exampleembodiment. Example embodiments may vary and are not limited to theequations shown above.

A baseline load ρ_(b) can be solved for using equation (7) above:

$\rho_{b} = {\lambda_{b}{\left\{ \frac{F}{B_{b} \cdot S} \right\}.}}$

For a certain baseline load ρ_(b), any total traffic intensity (λ_(b))can be made possible by properly scaling the baseline bandwidth B_(b).

As shown above in equation (6), the average delay time is based on anaverage service time X_(n) and an average waiting time. The averageservice time generally depends on the mobile terminal's 130 file sizeand realized Signal to Interference plus Noise Ratio (SINR). The SINRdistribution may be induced by a wireless network geometry incorporatingpath loss and shadow fading, and is represented by the random variable Sin the equations above.

If the pricing policy is based on average delay, such as Pricing Policy1, uniform allocation may perform nearly as well as an optimaldistribution calculated using the equations above. Therefore, the queuecontroller 210 may use a uniform allocation to distribute mobileterminals 130 amongst the priority queues, instead of calculating thetraffic intensity associated with each priority queue (λ₁, λ₂ . . . ,λ_(N)). This may simplify S320 above, for example, as the queuecontroller 210 may evenly distribute the total traffic intensity (λ_(b))into each priority queue.

Policy 2: P-th percentile Delay

In Policy 2, the fractional traffic intensities (λ₁, λ₂ . . . , λ_(N))and the P-th percentile delays T₁ ^(P), T₂ ^(P), . . . , T_(N) ^(P) arevariables of the utility function:

$\begin{matrix}{{{maximize}\mspace{14mu} {U\left( {\lambda_{1},\ldots \mspace{14mu},\lambda_{N},T_{1}^{P},\ldots \mspace{14mu},T_{N}^{P}} \right)}\overset{\overset{Revenue}{}}{c{\sum\limits_{i = 1}^{N}\frac{\lambda_{i}}{T_{i}^{P}}}}}{over}} & (10) \\{{{\lambda_{n} \in {\mathbb{R}}^{+}},{n = 1},\ldots \mspace{14mu},N}{{subject}\mspace{14mu} {to}\text{:}}} & (11) \\{{\sum\limits_{i = 1}^{N}\lambda_{i}} = \lambda_{b}} & (12) \\{{B = {\alpha \cdot B_{b}}},{0 < \alpha \leq 1}} & (13) \\{{{\underset{\underset{{Probability}\mspace{14mu} {Approximation}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} P\text{-}{th}\mspace{14mu} {Percentile}\mspace{14mu} {Delay}}{}}{\sum\limits_{i = 0}^{m\; i\; n{\{{{\lfloor\frac{T_{n}^{p}}{\Delta \; i}\rfloor},N_{S}}\}}}\left( {{p_{S}\lbrack i\rbrack} \cdot \left( {1 - {\rho_{n}^{{- \gamma_{n}} \cdot {({T_{n}^{p} - {{ \cdot \Delta}\; t}})}}}} \right)} \right)} \approx {{\mathbb{P}}\left\{ {\tau_{n} \leq T_{n}^{P}} \right\}}} = P},{{{for}\mspace{14mu} n} = 1},2,\ldots \mspace{14mu},N} & (14)\end{matrix}$

In Policy 2,

+ indicates all positive real numbers and c, λ_(b), B, α and B_(b) areas defined in Policy 1. Moreover, p_(S)[i], N_(S) and Δt are,respectively, the components, a number of components of a probabilitymass function (PMF) associated with a service time, and a resolution ofthe PMF associated with the service time. p_(S)[i], N_(S) and Δt may bemeasured beforehand and stored in the computer system according to knownmethods.

The PMF of the service time may be computed using the simulation of thewireless network as described in Policy 1. τ_(p) is the random variablerepresenting the delay for queue n. As an example, if the P-thpercentile delay is the 95-th percentile delay, P=0.95 in equation (14).

The variables γ_(n) and ρ_(n) are calculated using statistics of thewaiting time, for example using equations (27) and (28), which arediscussed in greater detail below. For example, the probability densityfunction (PDF) and cumulative distribution function (CDF) of the waitingtimes may be approximated by degenerated hyper-exponential distributionfunctions, as discussed below with regard “Statistics of the WaitingTime.”

Policy 3: Percentile Truncated Average Delay

In Policy 3, the fractional traffic intensities (λ₁, λ₂ . . . , λ_(N)),the average delays T ₁ ^(T) ⁰ , T ₂ ^(T) ⁰ , . . . , T _(N) ^(T) ⁰ ofthe prioritized queuing system truncated to the P₀-th percentile delayT₀ of the non-prioritized baseline system, and fractions of traffic P₁,P₂, . . . , P_(N) in each priority queue with delays less than T₀ arevariables of the utility function:

$\begin{matrix}{{{{maximize}\mspace{14mu} {U\begin{pmatrix}{\lambda_{1},\ldots \mspace{14mu},\lambda_{N},P_{1},\ldots \mspace{14mu},} \\{P_{N},{\overset{\_}{T}}_{1}^{T_{0}},\ldots \mspace{14mu},{\overset{\_}{T}}_{N}^{T_{0}}}\end{pmatrix}}} = \overset{\overset{Revenue}{}}{c{\sum\limits_{i = 1}^{N}\frac{P_{i}\lambda_{i}}{{\overset{\_}{T}}_{i}^{T_{0}}}}}}{over}} & (15) \\{{{\lambda_{n} \in {\mathbb{R}}^{+}},{n = 1},\ldots \mspace{14mu},N}{{subject}\mspace{14mu} {to}\text{:}}} & (16) \\{{\sum\limits_{i = 1}^{N}\lambda_{i}} = \lambda_{b}} & (17) \\{{B = {\alpha \cdot B_{b}}},{0 < \alpha \leq 1}} & (18) \\{{\underset{\underset{{Probability}\mspace{14mu} {Approximation}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} P_{0}\text{-}{th}\mspace{14mu} {Percentile}\mspace{14mu} {Delay}}{}}{\sum\limits_{i = 1}^{m\; i\; n{\{{{\lfloor\frac{T_{0}}{\Delta \; t}\rfloor},N_{S}}\}}}\left( {{p_{S}\lbrack i\rbrack} \cdot \left( {1 - {\rho_{0}^{{- \gamma_{0}} \cdot {({T_{0} - {{ \cdot \Delta}\; t}})}}}} \right)} \right)} \approx {{{\mathbb{P}}\left\{ {\tau_{0} \leq T_{0}} \right\}} + P_{0}}},\left( {{{Non}\text{-}{prioritized}},{{baseline}\mspace{14mu} {system}}} \right)} & (19) \\{{P_{n} = {{{\mathbb{P}}\left\{ {\tau_{n} \leq T_{0}} \right\}} \approx \underset{\underset{{Probability}\mspace{14mu} {Approximation}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} P_{n}\text{-}{th}\mspace{14mu} {Percentile}\mspace{14mu} {Delay}}{}}{\sum\limits_{i = 0}^{m\; i\; n{\{{{\lfloor\frac{T_{0}}{\Delta \; t}\rfloor},N_{S}}\}}}\left( {{p_{S}\lbrack i\rbrack} \cdot \left( {1 - {\rho_{n}^{{- \gamma_{n}} \cdot {({T_{0} - {{ \cdot \Delta}\; t}})}}}} \right)} \right)}}},{n = 1},2,\ldots \mspace{14mu},N,} & (20) \\{{{\overset{\_}{T}}_{n}^{T_{0}}\underset{\underset{{Truncated}\mspace{14mu} {Average}\mspace{14mu} {Approximation}}{}}{\approx {\overset{m\; i\; n{\{{{\lfloor\frac{{\overset{\_}{T}}_{0}}{\Delta \; t}\rfloor},N_{S}}\}}}{\sum\limits_{i = 0}}\left\lbrack {{p_{S,n}\lbrack i\rbrack} \cdot \begin{pmatrix}{\frac{{\left( {1 - \rho_{n}} \right) \cdot i \cdot \Delta}\; t}{1 - {\rho_{n}^{{- \gamma_{n}} \cdot {({T_{0} - {{ \cdot \Delta}\; t}})}}}} + \ldots +} \\\frac{\rho_{n} \cdot \begin{pmatrix}{1 + {{\gamma_{n} \cdot i \cdot \Delta}\; t} -} \\{\left( {1 + {\gamma_{n}T_{0}}} \right) \cdot ^{{- \gamma_{n}} \cdot {({T_{0} - {{ \cdot \Delta}\; t}})}}}\end{pmatrix}}{\gamma_{n} \cdot \left( {1 - {\rho_{n}^{{- \gamma_{n}} \cdot {({T_{0} - {{ \cdot \Delta}\; t}})}}}} \right)}\end{pmatrix}} \right\rbrack}}},{n = 1},\ldots \mspace{14mu},{N.}} & (21)\end{matrix}$

In Policy 3, c, λ_(b), B, α, B_(b), p_(S)[i], N_(S), Δt, γ_(n), ρ_(n)and τ_(n) are as defined in Policy 1 and Policy 2. The variables γ₀ andρ₀ are also calculated using statistics of the waiting time as discussedin Policy 2, and τ₀ is the random variable representing the delay forthe baseline, non-prioritized system. As an example, if the P₀-thpercentile delay is the 95-th percentile delay, P₀=0.95 in equation(19).

While example embodiments have been particularly shown and described, itwill be understood by one of ordinary skill in the art that variationsin form and detail may be made therein without departing from the spiritand scope of the claims.

Statistics of the Waiting Time

As discussed above, the variables γ_(n) and ρ_(n) are calculated usingstatistics of the waiting time. For example, the probability densityfunction (PDF) and cumulative distribution function (CDF) of the waitingtimes may be approximated by degenerated hyper-exponential distributionfunctions. However, example embodiments may vary and are not limited tothe example embodiments discussed above.

The Laplace-Stieltjes transform (LST) of the waiting time distributionfunction may be given by:

$\begin{matrix}{{W*(S)} = \frac{\left( {1 - {\lambda \; s}} \right)s}{s - \lambda + {\lambda \; B*(s)}}} & (22)\end{matrix}$

A closed form expression for the waiting time LST requires the servicetime LST, B*(s), to be known. Unfortunately, an analytically tractableexpression for B*(s) is not known. Hence, we may use degeneratedhyper-exponential distributions to approximate the PDF and CDF for thewaiting time. However, as discussed above, these equations are providedto illustrate a particular example embodiment. Example embodiments mayvary and are not limited to the equations shown.

In this sense, we have for the PDF:

$\begin{matrix}{{f_{W}(w)} = \left\{ {\begin{matrix}{{{\left( {1 - \rho} \right){\delta (w)}} + {\rho \; \gamma \; ^{{- \gamma}\; w}}},} & {{{for}\mspace{14mu} w} \geq 0} \\{0,} & {elsewhere}\end{matrix},{{{with}\mspace{14mu} \gamma} \geq {0\mspace{14mu} {and}\mspace{14mu} 0} \leq \rho \leq 1},} \right.} & (23)\end{matrix}$

where δ(w) is the Dirac delta function.

Moreover, the CDF is given by

$\begin{matrix}{{F_{W}(t)} = {{P\left\{ {W \leq t} \right\}} = {{\int_{0}^{t}{{f(w)}{w}}} = \left\{ {\begin{matrix}{{1 - {\rho }^{{- \gamma}\; t}},} & {{{for}\mspace{14mu} t} \geq 0} \\{0,} & {elswhere}\end{matrix},{{with}\mspace{14mu} t},{\gamma \geq {0\mspace{14mu} {and}\mspace{14mu} 0} \leq \rho \leq 1},} \right.}}} & (24)\end{matrix}$

In a prioritized system, the PDF and CDF of the waiting times of eachclass n=1, 2, . . . N can be modeled by a version of the functionsabove, i.e.:

$\begin{matrix}{{f_{W,n}(w)} = \left\{ {\begin{matrix}{{{\left( {1 - \rho_{n}} \right){\delta (w)}} + {\rho_{n}\gamma_{n}^{{- \gamma_{n}}w}}},} & {{{for}\mspace{14mu} w} \geq 0} \\{0,} & {elsewhere}\end{matrix},{{{with}\mspace{14mu} \gamma_{n}} \geq {0\mspace{14mu} {and}\mspace{14mu} 0} \leq \rho_{n} \leq 1},} \right.} & (25) \\{{F_{W,n}(t)} = {{P\left\{ {W_{n} \leq t} \right\}} = \left\{ {\begin{matrix}{{1 - {\rho_{n}^{{- \gamma_{n}}t}}},} & {{{for}\mspace{14mu} t} \geq 0} \\{0,} & {elsewhere}\end{matrix},{{{with}\mspace{14mu} \gamma_{n}} \geq {0\mspace{14mu} {and}\mspace{14mu} 0} \leq \rho_{n} \leq 1},} \right.}} & (26)\end{matrix}$

where the parameters and can be computed as

$\begin{matrix}{{\rho_{n} = \frac{2{\overset{\_}{W}}_{n}^{2}}{\overset{\_}{W_{n}^{2}}}},{and}} & (27) \\{{\gamma_{n} = \frac{2\overset{\_}{W_{n}}}{\overset{\_}{W_{n}^{2}}}},} & (28)\end{matrix}$

where W_(n) is the average waiting time for class n, and the secondmoment of the waiting time W_(n) ² for class is given as:

$\begin{matrix}{{\overset{\_}{W_{n}^{2}} = {\frac{\sum\limits_{i = 1}^{N}{\lambda_{i}\overset{\_}{X_{i}^{3}}}}{3\left( {1 - {\sum\limits_{i = 1}^{n - 1}{\lambda_{i}\overset{\_}{X_{i}}}}} \right)^{2}\left( {1 - {\sum\limits_{i = 1}^{n}{\lambda_{i}\overset{\_}{X_{i}}}}} \right)} + \frac{\left( {\sum\limits_{i = 1}^{n}{\lambda_{i}\overset{\_}{X_{i}^{2}}}} \right)\left( {\sum\limits_{i = 1}^{N}{\lambda_{i}\overset{\_}{X_{i}^{2}}}} \right)}{2\left( {1 - {\sum\limits_{i = 1}^{n - 1}{\lambda_{i}\overset{\_}{X_{i}}}}} \right)^{2}\left( {1 - {\sum\limits_{i = 1}^{n}{\lambda_{i}\overset{\_}{X_{i}}}}} \right)^{2}} + \frac{\left( {\sum\limits_{i = 1}^{n - 1}{\lambda_{i}\overset{\_}{X_{i}^{2}}}} \right)\left( {\sum\limits_{i = 1}^{N}{\lambda_{i}\overset{\_}{X_{i}^{2}}}} \right)}{2\left( {1 - {\sum\limits_{i = 1}^{n - 1}{\lambda_{i}\overset{\_}{X_{i}}}}} \right)^{3}\left( {1 - {\sum\limits_{i = 1}^{n}{\lambda_{i}\overset{\_}{X_{i}}}}} \right)}}},} & (29)\end{matrix}$

and X_(n) , X_(n) ² , X_(n) ³ , n=1, . . . , N, are, respectively, theaverages, the second moments and the third moments of the service times.Moreover, X_(n) , X_(n) ² , n=1, . . . , N, are given by equations (7)and (8), respectively, and X_(n) ³ is given as:

$\begin{matrix}{{\overset{\_}{X_{n}^{3}} = {{\left\{ \left( \frac{F}{B \cdot S} \right)^{3} \right\}} = {{\frac{F^{3}}{B^{3}} \cdot }\left\{ \frac{1^{3}}{S} \right\}}}},{n = 1},\ldots \mspace{14mu},N,{with}} & (30) \\{{\left\{ \frac{1^{3}}{S} \right\}} \approx 7.75} & (31)\end{matrix}$

However, these equations are provided to illustrate a particular exampleembodiment. Example embodiments may vary and are not limited to theequations shown above.

Observe that the conditions γ_(n)≧0 and 0≦ρ_(n)≦1 implies that

2 {overscore (W _(n))}²≦ W _(n) ² , W _(n) ≧0 and W _(n) ²≧0,ƒ or n=1,2,. . . ,N  (32)

must be fulfilled in order for the approximation by the degeneratedhyper-exponential distribution to be valid. Moreover, choosing γ_(n) andρ_(n) as (27) and (28), respectively, the average and second moment ofƒ_(W,n)(w) are equal to W_(n) and W_(n) ² , n=1, . . . , N,respectively.

Because the delay is defined as T_(n)=(1/μ_(n))+W_(n) (i.e., the sum ofwaiting time and service time), its PDF is given by the convolution ofthe waiting time PDF with the service time distribution function:

ƒ_(T,n)(t)=ƒ_(W,n(t))*ƒ_(S,n)(t).  (33)

For numeric computation purposes, we consider the PDF of the servicetime to be sampled to a discrete probability mass function (PMF) ofsufficient resolution, i.e.:

P _(S,n)(k·Δt)=Σ_(i=0) ^(N) ^(S) p _(S,n) [i]·δ(k−1),k=0,1, . . . ,N_(S),  (34)

where Δt is the time resolution of the PMF, N_(S) is the number ofcomponents in the PMF, δ(·) is the Dirac delta function and n=1, 2, . .. , N.

Hence, the convolution in equation (33) can be written as:

ƒ_(T,n)(t)=Σ_(i=0) ^(N) ^(S) p _(S,n) [i]·ƒ _(W,n)(t−i·Δt).  (35)

Therefore, the CDF of the delays are given by:

$\begin{matrix}{{F_{T,n}(t)} = {{P\left\{ {T_{n} \leq t} \right\}} = {{\int_{0}^{t}{{f_{T,n}(\tau)}{\tau}}} = {{\int_{0}^{t}{\sum\limits_{i = 0}^{m\; i\; n{\{{{\lbrack\frac{t}{\Delta \; t}\rbrack},N_{S}}\}}}{{{p_{S,n}\lbrack i\rbrack} \cdot {f_{W,n}\left( {\tau - {{i \cdot \Delta}\; t}} \right)}}{\tau}}}} = {{\sum\limits_{i = 0}^{m\; i\; n{\{{{\lbrack\frac{t}{\Delta \; t}\rbrack},N_{S}}\}}}\left( {{p_{S,n}\lbrack i\rbrack} \cdot {\int_{{i \cdot \Delta}\; t}^{t}{{f_{W,n}\left( {\tau - {{i \cdot \Delta}\; t}} \right)}{\tau}}}} \right)} = {{\sum\limits_{i = 0}^{m\; i\; n{\{{{\lbrack\frac{t}{\Delta \; t}\rbrack},N_{S}}\}}}\begin{pmatrix}{{{p_{S,n}\lbrack i\rbrack} \cdot {\int_{{i \cdot \Delta}\; t}^{t}{\left( {1 - \rho_{n}} \right)\delta \left( {\tau - {{i \cdot \Delta}\; t}} \right)}}} +} \\{\rho_{n}\gamma_{n}^{{- \gamma_{n}} \cdot {({\tau - {{ \cdot \Delta}\; t}})}}{\tau}}\end{pmatrix}} = {\sum\limits_{i = 0}^{m\; i\; n{\{{{\lbrack\frac{t}{\Delta \; t}\rbrack},N_{S}}\}}}\left( {{p_{S,n}\lbrack i\rbrack} \cdot \left( {\rho_{n}^{{- \gamma_{n}} \cdot {({t - {{ \cdot \Delta}\; t}})}}} \right)} \right)}}}}}}} & (36)\end{matrix}$

What is claimed is:
 1. A method of operating a network, the methodcomprising: receiving a measurement of total traffic intensity;receiving an expected quality of service associated with a packet; andassigning the packet to one of two or more priority queues based on themeasurement of total traffic intensity and the expected quality ofservice, the two or more priority queues having different delay metrics.2. The method of claim 1, further comprising: switching the packet tothe one of the two or more priority queues by a switch.
 3. The method ofclaim 1, further comprising: measuring the total traffic intensity,wherein the receiving receives the measured total traffic intensity. 4.The method of claim 1, further comprising: determining a trafficintensity associated with each of the two or more priority queues andthe delay metric associated with each of the two or more priority queuesbased on the measurement of total traffic intensity, wherein theassigning assigns the packet to the one of two or more priority queuesbased on the expected quality of service and the determined trafficintensity associated with each of the two or more priority queues. 5.The method of claim 1, wherein the expected quality of service includesa requested priority from a user, the requested priority being one oftwo or more priority levels from which the user selects.
 6. The methodof claim 5, wherein the receiving the expected quality of serviceassociated with the packet further comprises: receiving an expectedquality of service associated with a mobile terminal; receiving thepacket from the mobile terminal; and associating the packet with theexpected quality of service associated with the mobile terminal.
 7. Themethod of claim 4, further comprising: determining a price of servicefor the packet based on the determined the delay metric associated withthe one of two or more priority queues.
 8. The method of claim 7,wherein the delay metric is an average delay and the determining theprice determines the average delay based on an average service time andan average waiting time.
 9. The method of claim 7, wherein the delaymetric is a P-th percentile delay and the determining the pricedetermines the P-th percentile delay based on a probabilityapproximation including a waiting time for the one of two or morepriority queues, a number of components of a probability mass function(PMF) associated with a service time, and a resolution of the PMFassociated with the service time.
 10. The method of claim 7, wherein thedelay metric is a truncated average delay approximation and thedetermining the price determines the truncated average delayapproximation based on a waiting time for the one of two or morepriority queues and a delay for the non-prioritized system.
 11. Anetwork, the network comprising: a queue controller configured toreceive a measurement of total traffic intensity, to receive an expectedquality of service associated with a packet, and to assign the packet toone of two or more priority queues based on the measurement of totaltraffic intensity and the expected quality of service, the two or morepriority queues having different delay metrics.
 12. The network of claim11, further comprising: a switch configured to switch the packet to theone of two or more priority queues.
 13. The network of claim 11, furthercomprising: a traffic intensity measurement device configured to measurethe total traffic intensity and to transmit the total traffic intensityto the queue controller.
 14. The network of claim 11, wherein the queuecontroller is further configured to determine a traffic intensityassociated with each of the two or more priority queue and the delaymetric associated with each of the two or more priority queues based onthe measurement of total traffic intensity, and the queue controller isconfigured to assign the packet to the one of two or more priorityqueues based on the expected quality of service and the determinedtraffic intensity associated with each of the two or more priorityqueues.
 15. The network of claim 11, wherein the expected quality ofservice includes a requested priority from a user, the requestedpriority being one of two or more priority levels from which the userselects.
 16. The network of claim 15, wherein the queue controller isfurther configured to receive an expected quality of service associatedwith a mobile terminal, to receive the packet from the mobile terminaland to associate the packet with the expected quality of serviceassociated with the mobile terminal.
 17. The network of claim 14,wherein the queue controller is configured to determine a price ofservice for the packet based on the determined delay metric associatedwith the one of two or more priority queues.
 18. The network of claim17, wherein the delay metric is an average delay and the queuecontroller is configured to determine the average delay based on anaverage service time and an average waiting time.
 19. The network ofclaim 17, wherein the delay metric is a P-th percentile delay and thequeue controller is configured to determine the P-th percentile delaybased on a probability approximation including a waiting time for theone of two or more priority queues, a number of components of aprobability mass function (PMF) associated with a service time, and aresolution of the PMF associated with the service time.
 20. The networkof claim 17, wherein the delay metric is a truncated average delayapproximation and the queue controller is configured to determine thetruncated average delay approximation based on a waiting time for theone of two or more priority queues and a delay for the non-prioritizedsystem.